For months, Rev. Samuel Rodriguez, the influential head of the National Hispanic Christian Leadership Conference, complained that the Republican primary was alienating conservative Latino voters. “They don’t want us,” he told me in February, after specifically criticizing Mitt Romney and other candidates for their unvarnished get-tough immigration rhetoric.

But now Rodriguez says the Romney campaign is beginning to make amends. “I have noticed a very significant change,” Rodriguez told me Monday. “It’s really night and day.”

In recent weeks, Rodriguez explained, two senior Romney staffers, Peter Flaherty and Mark DeMoss, who lead conservative and religious outreach for the campaign, have opened a private dialog with him aimed at restarting the relationship between Romney and the 16 million Latino evangelicals in America. A Romney campaign official told TIME on Tuesday that the campaign is seeking an in-person meeting between Rodriguez and Romney in the coming weeks.

“I can tell you the Romney campaign assured me of the importance of the Hispanic community as it concerns the future of this nation and even the future of the conservative movement,” Rodriguez said. “They understand it. They affirmed it. They celebrated it.”

But the Romney campaign still faces significant hurdles in winning over the Latino vote, a fact that was on stark display in Washington on Tuesday at the Republican National Committee offices, where officials debuted their plans to win Latino support for the Romney campaign. In the coming weeks, six outreach directors will be dispatched to key swing states to drum up support among Latinos. “What we are trying to do is rebuild the relationship to let them know that we do care about the Hispanic community,” said Bettina Inclan, the coordinator of the party’s effort. “We haven’t done enough to reach out to them.”

At one point, she attacked President Obama’s record on immigration. “The reality is that this President has deported more immigrants than any other president in history,” she said. But when asked if Republicans supported more or less deportations she did not have an answer. “I think that as a candidate, to my understanding that he’s still deciding what his position on immigration is, so I can’t talk about what his proposal is going to be because I don’t know,” she said.

Reporters covering the event tweeted out her comments, and within minutes the Obama campaign and its liberal supporters jumped on them as evidence that Romney was trying to run away from hardline positions–no amnesty for illegal immigrants, strict ID checks at all places of employment–that he had promoted during his primary campaign. Before the press briefing ended, Kirsten Kukowski, a Republican party spokeswoman, walked back Inclan’s quote. “We never said the governor is still deciding on immigration,” Kukowski said, even though Inclan had just said that. Within a couple of hours, Inclan withdrew her comment via her own Twitter account. “I misspoke,” she said. “Romney’s position on immigration is clear.”

Rodriguez hopes that there is still some wiggle room in that position. In particular, he has told the campaign that he hopes Romney will support a proposal that has been put forward by Florida Senator Marco Rubio that would grant legal status short of citizenship to undocumented immigrants who come to the U.S. as children and attend college or join the military. Rodriguez says he also hopes that the campaign will appoint its own Latino outreach director to work with the community.

As a pastor, Rodriguez does not endorse candidates. But in 2004 he played a major role in working with Republicans to turnout socially conservative Latino voters, driving up President Bush’s numbers among Latinos to an estimated 40% to 44%, a recent record for the GOP. The National Hispanic Christian Leadership Conference organizes large-scale voter registration drives in its member churches, and encourages parishioners to follow the Bible’s teachings about life and marriage in the voting booth.

Rodriguez said he would still like to see the Romney campaign go further than the Rubio proposal by proposing full citizenship for the undocumented children of illegal immigrants, a plan that President Obama and many Democrats support. But he said that even embracing the Rubio proposal, which Romney’s campaign is studying, would be a “ginormous step.”

Still, Rodriguez added, the Romney campaign has a long way to go. For the better part of a year, the Obama campaign has been running an aggressive Latino outreach effort of its own, and in recent weeks it has been advertising on Spanish-language television. The Romney campaign must play catch-up after spending much of the last year running to the right of many Republicans on immigration, while doing little Latino outreach at all outside the state of Florida. “The Romney campaign is still far behind,” said Rodriguez. But he also said that his recent conversations with the campaign gave him hope that the gap could be closed. “It provides a great platform for us to go forward from,” he said.